I do not have this game, but asked the same question, and was told yes, that you can dance on the carpet. The important thing to consider would be if you can move your feet quickly on the carpet without them catching and making you fall.
I have the game and I think doing it on the carpet is difficult in barefeet, because you have to move pretty quick. Probably shoes on carpet would give more traction, just socks would slip around too much. I put down a plastic mat that we had under our treadmill and it works with barefeet pretty good.
I have the game and use it every day on my carpeted living room floor. It is very hard to dance on the carpeted floor, and it can hurt your knees. I have modified some of the moves so my knees aren't strained. I also found some socks that slip a little better on the carpet so that has helped too. Either way, the game is a lot of fun, the music is great (if you like Latin and world music), and it keeps me motivated. I've used it for 30 minutes to 1 1/2 hours every day for about three weeks. I haven't lost any weight (probably need to change diet), but I have lost an inch around my ass!
If you have to do it on carpet make sure your shoes have a smooth bottom. I do Zumba at the gym 2x a week and the room is carpeted. The instructor always teaches newbies how to move to prevent injury to knees and ankles. If your shoe has too much tread on the bottom it'll catch on the carpet and could cause a knee injury. I wear Sansha dance shoes for Zumba. The bottoms are smooth. They're similar to these. If you plan to do a lot of dancing on carpet they're worth the investment. Sansha Motion Dance Sneaker
Is special programming of the remote required for this game? The reason I ask is that no matter how hard I try with the mid-intensity routines, I never seem to burn more than 60 calories and I never get any stars! Its maybe an ego thing as I do get a good sweat but, just wondering ...